System of Estimating the Cross-Sectional Area of a Molecule for Use in the Prediction of Ion Mobility

ABSTRACT

A method of estimating the cross-sectional area of a molecule for use in the prediction of ion mobility gives gas phase interaction radii determination and cross-sectional algorithm computation to provide separation and characterisation of structurally related isomers. More specifically, the invention provides a method of correlating the differences in the molecular structures with differences in anti-cancer activity of pre-determined anti-cancer drugs by utilizing a new algorithm for estimating the cross-sectional area of the molecules of such drugs.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No. of13/264,042 filed on Feb. 3, 2012, pending, which is a National Stage ofInternational Application No. PCT/GB2010/050630 filed on Apr. 15, 2010which claims priority from and the benefit of United Kingdom PatentApplication No. 0906466.8 filed on Apr. 15, 2009 and United KingdomPatent Application No. 0906467,6 filed Apr. 15, 2009 and U.S.Provisional Patent Application Ser. No. 61/185,337 filed on Jun. 9,2009. The entire contents of these applications are incorporated hereinby reference.

BACKGROUND TO THE INVENTION

This invention relates to a method of estimating the cross-sectionalarea of a molecule for use in the prediction of ion mobility for a widerange of molecular species.

Ion mobility has the potential to separate isomeric species based ondifferences in gas phase collision cross-sections (Ω) and can providevaluable information on ionic conformation through comparisons withtheoretical models, However, to relate the ion mobility derivedcollision cross-section of a molecule to its structure accurately, it isnecessary to obtain prior knowledge of the gas phase radii of theconstituent atoms.

The molecular cross-section is approximated as the rotationally averagedarea of the “shadow” cast by the molecule. The term “shadow” is used torefer to the protection of a molecule, atom or ellipsoid onto any plane.The plane employed remains fixed throughout the calculation.

The projection approximation (PA) has been shown to be a useful methodof calculating the cross-section of a molecule to be used in theprediction of ion mobility. It is not possible to calculate theprojection approximation cross-section directly, but it is possible toobtain numerical approximations using Monte Carlo techniques. MonteCarlo methods are a class of computational algorithms that rely onrepeated random sampling to compute their results and often are usedwhen it is infeasible or impossible to compute an exact result with adeterministic algorithm.

It is known to obtain prior knowledge of the gas phase radii of theconstituent atoms of a molecule by means of an algorithm known as MobCal(http://www.indiana.edu/˜nano.Software.html) which includes thefollowing steps:

(1) Set A=O, n=O, and(2) select a random orientation of the molecule(3) select a rectangle bounding the molecular shadow and calculate thearea of therectangle=area Abox,(4) select a point randomly within the rectangle,(5) if the point lies within the molecular shadow, then A=A+Abox(6) n=n+1(7) if n <n_(max) GOTO 2

(i.e. select another random orientation of the molecule for the nextiteration)

(8) End, Result is A/n

However, there are at least two potential (but related) problems withthis approach. First, in the selection of n_(max), it is difficult ifnot impossible to know how many orientations (step 2) are sufficient,and secondly there are situations in which convergence is slow so thatnaive convergence tests can be misleading.

The above algorithm can be improved to allow more than one selection perorientation giving a modified algorithm.

SUMMARY OF THE INVENTION

One aspect or feature of the invention provides a method of estimatingthe cross sectional area of a molecule, e.g. for determining thecharacteristics of predetermined or sample molecules, the method thesteps of:

(1) Set A=O, n=O, and(2) select a random orientation of the molecule(3) select a rectangle bounding the molecular shadow and calculate thearea of the rectangle=area Abox(4) select K points randomly within the rectangle(5) for each point that lies in the molecular shadow, A=A+Abox/K(6) n=n+1(7) if n<n_(max) GOTO 2 (next iteration)(8) End. Result is A/n

The above method will be referred to hereinafter as the ‘rectangle’method.

However, the present invention also involves the use of a newlydeveloped collisional cross-sectional (CCS) algorithm which is a highlyefficient implementation of the projection approximation that utilises anovel sampling technique to provide improved confidence in convergenceof the rotationally averaged cross section, obtained to a user-specifiedaccuracy.

Another aspect of the present invention provides a method of estimatingthe cross sectional area of a molecule, e.g. for determining thecharacteristics of predetermined or sample molecules, the methodcomprising the steps of:

A) Predicting the geometric structure of the molecule of interest;

B) Assigning a value for the cross sectional area of each atom withinthe molecule;

C) Calculating the sum of the values of the cross sectional area foreach atom within the molecule;

D) Randomly selecting an orientation of the predicted geometricstructure of said molecule of interest;

E) Randomly selecting one or more atoms with probability proportional tothe atoms cross sectional area;

F) Randomly selecting a position within the cross sectional area of the,or each of, the selected atom(s),

G) Identify the number of atoms whose cross sectional area includes saidrandomly selected position;

H) Calculating a value for the cross sectional area of said molecule ofinterest at said randomly selected orientation;

I) Calculate an averaged cross sectional area over all said randomlyselected orientations;

J) Iterate steps D) to I) for at least N iterations and/or until Mindependent calculations of the averaged cross sectional area agreewithin a predetermined range R for X iterations

The above method will be referred to hereinafter as the ‘importancesampling’ method.

According to a feature of the invention the value of N may be between 0and 50, for example between 0 and 30 or between 20 and 50 or between 10and 40.

According to another feature of the invention the value of M may bebetween 1 and 20, for example between 1 and 10 or 1 and 5 oralternatively between 10 and 20 or 15 and 20 or alternatively between 5and 15.

According to another feature of the invention the value of R may bebetween 0.1 and 20%, for example 1 and 20% or alternatively between 0,1and 1%.

[Note That R Can be a Percentage or an Absolute Value]

According to another feature of the invention the value of X may bebetween 1 and 20, for example between 1 and 10 or 1 and 5 oralternatively between 10 and 20 or 15 and 20 or alternatively between 5and 15 .

Another aspect of the invention provides a method of determiningcharacteristics of predetermined molecules (e.g. small molecules andproteins, peptides, oligoneucleotides and glycans) comprising the use ofa combined ion mobility—mass spectrometry (IM-MS) technique forexperimentally determining a range of molecular structures and comparingvalues of that range with those derived by an estimating methodaccording to any of the five immediately preceding paragraphs so as tocorrelate the differences in the molecule structures with differences inselected predetermined activity of those molecules.

According to a feature of this aspect of the invention, the method maycorrelate the differences in the molecular structures with differencesin anti-cancer activity of predetermined anti-cancer drugs. Preferably,the anti cancer drugs are organometallic based drugs. Preferably, theorganometallic drugs are isomeric Ru-based.

According to another feature of this aspect of the invention, the IM-MStechnique may include the use of travelling wave (T-wave) mobilityseparation.

The method of the present invention gives gas phase interaction radiidetermination and cross-section algorithm computation to provideseparation and characterisation of structurally related isomers by ionmobility.

A further aspect of the invention provides a system for determiningcharacteristics of predetermined molecules, the system comprising an onmobility cell, a mass spectrometer and a processor programmed orconfigured to determine experimentally a range of molecular structuresand compare values of that range with those derived by an estimating amethod described above so as to correlate the differences in themolecular structures with differences in selected predetermined activityof those molecules.

A yet further aspect of the invention provides a computer programelement comprising computer readable program code means for causing aprocessor to execute a procedure to implement the method describedabove.

The computer program element may be embodied on a computer readablemedium.

A yet further aspect of the invention provides a computer readablemedium having a program stored thereon, where the program is to make acomputer execute a procedure to implement the method as described above.

BRIEF DESCRIPTION OF THE DRAWING

An embodiment of the invention will now be described, by way of exampleonly, with reference to the accompanying drawing, wherein:

FIG. 1 is a flow chart illustrating an algorithm according to anembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

One algorithm of the present invention is as follows:(1) Amax=sum over π*R_(i)*R_(i) wherein R_(i) is the radius of the i'thatom(2) Set A=0, n=0, and(3) then select a random orientation of the molecule(4) select K atoms at random with probability proportional to the atom'scross sectional area(5) then select a point with uniform probability within the circularshadow of each selected atom, and(6) for each thus selected point,

A=A+Amax/(m*K)

Where m is the number of atoms with shadows overlapping the point

(7) n=n+1(8) if n<n_(max) GOTO 3 (next iteration)(9) End. Result is A/nFor many molecules, this importance sampling algorithm will converge tothe desired result faster than that of the prior art algorithms referredto.The following termination procedure has been implemented in conjunctionwith the above algorithm:(1) Instantiate N projection approximation calculations (henceforthcalled objects)(2) perform iterations for each of these objects in turn, keepingrunning area estimates for each object,(3) terminate when the area estimates for all objects agree with a userspecified tolerance (either percentage or absolute), reporting theoverall average of these estimates as the result.

It may be advantageous to use a mixture of objects utilizing both theprior art algorithms referred to and the algorithm of the presentinvention to achieve confidence in the termination.

This newly developed CCS algorithm is a highly efficient implementationof the projection approximation that utilises a novel sampling techniqueto provide improved confidence in convergence of the rotationallyaveraged cross section, obtained to a user-specified accuracy.

The IMS device of a mass spectrometer was calibrated using a haemoglobinpeptide mixture and other compounds of known collisional cross section,such as polyglycine(http.//www.indiana.edu/˜clemmer/Research/research.htm); a calibrationcoefficient was then derived. The ion mobility of each small moleculewas measured and therefore the experimental collision cross sectiondetermined. The radius of each of the atoms, specific to an individualsmall molecule were then ‘tuned’ within the CCS algorithm such that theoutput of the CCS algorithm closely matched the experimentally derivedCCS values for each of the small molecules analysed. An optimalinteraction radius value (Á²) for C, H, O, S, Cl, F, N & Ru were thusderived.

The small molecules used to optimise the CCS algorithm were: C60, C70,pyrene, camphene, phenanthrene, triphenylene, naphthalene, ampicillin,spermine, lorazepam, caffeine, reserpine, raffinose, nifedipine,nimodipine, dexamethazone, diphenylhydramine, metoprolol, glutathione,cysteine, apomorphine, erythromycin, oxytetracyclin, veraparnil,salbutamol, acetylsalicylic acid, the 20 naturally occurring commonamino acids, angiotensin H, oxytocin, testosterone, ibuprofen,beta-cyclodextrin and the ruthenium containing compounds ru-ortho (andassociated HCl neutral loss species), ru-meta (and associated HClneutral loss species), ru-para (and associated HCl neutral lossspecies).

Ion mobility-mass spectrometry combined with molecular modelling for theseparation and configurational analysis of low-molecular-weight isomericorganorutheniurn anticancer complexes were separated using ion mobilitybased on travelling-wave technology and the experimentally determinedcollision cross sections were compared to theoretical calculations.

Certain organometallic drugs are used in the fight against cancer. Theplatinum-based drug, cisplatin [cis-diamminedichloridoplatinum(II)], forexample, falls into this category and is one of the leading drugs usedin the fight against cancer. DNA is a potential target for manymetal-based anticancer drugs and distortions of DNA structure oftencorrelate with anticancer activity. Other metal-based anticancer drugs,such as those based on ruthenium, are being developed as alternativetreatments to combat cancer. In particular, the aim is to widen thespectrum of anticancer activity, reduce unwanted side effects, and avoidcross-resistance with cisplatin and related drugs. insights into thephysical size and shape of these novel Ru-based drugs are important forelucidation of structure-activity relationships and for optimizing keyinteractions such as intercalation into DNA. Three novel isomericRu-based anticancer drugs have been explored using a combined ionmobility and mass spectrometry (IM-MS) approach together with anestimating method according to the invention.

As a stand-alone technique, MS cannot separate isomeric species orprovide bulk structural conformational information. However, IM has theability to rapidly separate isomeric species (on the MS acquisitiontimescale) based on differences in their collision cross sections (CCS;physical size and shape) in the gas phase, thus providing specificinformation on ionic configuration. The combination of IM with MSprovides an extremely powerful analytical tool.

To investigate the possible benefits of the IM-MS technique, aninstrument that is based around “traveling-wave” (T-wave) mobilityseparation was used to analyze a mixture of three low-molecular-weightisomeric ruthenium terphenyl anticancer complexes (m/z 427.1 based on¹⁰²Ru). Individual differences in shape have been studied in an attemptto correlate them with differences in anticancer activity. Molecularmodelling was also used to generate a so range of possible structuresand the theoretical CCSs for these structures were calculated forcomparison with experimentally derived T-wave values. Excellentagreement was observed between the experimentally and theoreticallyderived CCS measurements.

The ion mobility derived gas phase interaction radii in combination withthe new CCS algorithm, molecular modelling and ion mobility massspectrometry for the separation and conformational analysis of threelow-molecular-weight isomeric organoruthenium anti-cancer complexescontaining ortho-, meta- or para-terphenyl arena ligands (Mw -427,1) andthe subsequent isomeric HCl neutral loss species (Mw 391.1) has beenused in accordance with the invention, The six isomeric compounds showedwell defined arrival time distributions allowing experimental collisioncross-sections to be calculated and compared to theoretical values.Excellent agreement was observed between all experimentally- andtheoretically-derived results. The difference in shape of the elongatedterphenyl arena compared to the more compact shapes is likely to make animportant contribution to the significantly higher anti-cancer activityof the elongated structure.

In summary, the invention reports inferred gas phase interaction radiifor H, C, and the previously uninvestigated O, S, Cl, F, N, Fe, Pt andRu. Furthermore, the method of the present invention demonstrates forthe first time that isomeric ruthenium (II) terphenyl anticancercomplexes, whose CCSs differ by less than 9.0Á², can be separated andcharacterised by travelling wave ion mobility.

The table below shows results that were obtained using the Mobcalalgorithm as compared with the rectangle and importance samplingmethods.

Compound Rectangle Importance Sampling Caffeine 0.050 seconds 0.016seconds Ampicillin 0.042 seconds 0.031 seconds Spermine 0.090 seconds0.013 seconds

It will be appreciated by those skilled in the art that any number ofcombinations of the aforementioned features and/or those shown in theappended drawing provide clear advantages over the prior art and aretherefore within the scope of the invention described herein.

1. A system for determining characteristics of predetermined molecules,the system comprising: a sufficiently programmed computer; an ionmobility cell; a mass spectrometer; and a processor programmed orconfigured to determine experimentally, values of a range of molecularstructures and compare the values of the range with those derived by amethod of estimating a cross-sectional area of a molecule of interest soas to correlate differences in the molecular structures with differencesin selected predetermined activity of those molecules wherein saidmethod of estimating the cross sectional area of a molecule of interestcomprises the steps of: A) Developing a predicted geometric structure ofthe molecule of interest; B) Assigning a value for a cross sectionalarea of each atom within the molecule; C) Calculating a sum of values ofthe cross sectional area for each atom within the molecule; D) Randomlyselecting an orientation of the predicted geometric structure of saidmolecule of interest; E) Randomly selecting a number of atoms K with aprobability proportional to the atom's cross sectional area; F) Randomlyselecting a position within the cross sectional area of each of thenumber of atoms K; G) Identifying a number of atoms whose crosssectional area includes said position; H) Calculating a value for thecross sectional area of said molecule of interest at said orientationbased on the sum of values of the cross sectional area for each atomwithin the molecule divided by the number of atoms K times the number ofatoms m; I) Calculating an averaged cross sectional area over all saidrandomly selected orientations; and J) Iterating steps D) to I) for atleast N iterations or until M independent calculations of the averagedcross sectional area agree within a predetermined range R for Xiterations wherein at least steps D) to I) are preformed with thesufficiently programed computer.
 2. The system according to claim 1,wherein the value of N is between 1 and 50, the value of M is between 1and 20, the value of R is between 1 and 20% and the value of X isbetween 1 and
 20. 3. A system for determining characteristics ofpredetermined molecules, the system comprising: a sufficientlyprogrammed computer; an ion mobility cell; a mass spectrometer; and aprocessor programmed or configured to determine experimentally with acombined ion mobility-mass spectrometry (IM-MS) technique a range ofmolecular structures and compare the values of the range with thosederived by a method of estimating a cross-sectional area of a moleculeof interest so as to correlate differences in the molecular structureswith differences in selected predetermined activity of those moleculeswherein said method of estimating the cross sectional area of a moleculeof interest comprises the steps of: A) Developing a predicted geometricstructure of the molecule of interest; B) Assigning a value for a crosssectional area of each atom within the molecule; C) Calculating a sum ofvalues of the cross sectional area for each atom within the molecule; D)Randomly selecting an orientation of the predicted geometric structureof said molecule of interest; E) Randomly selecting a number of atoms Kwith a probability proportional to the atom's cross sectional area; F)Randomly selecting a position within the cross sectional area of each ofthe number of atoms K; G) identifying a number of atoms whose crosssectional area includes said position; H) Calculating a value for thecross sectional area of said molecule of interest at said orientationbased on the sum of values of the cross sectional area for each atomwithin the molecule divided by the number of atoms K times the number ofatoms m; I) Calculating an averaged cross sectional area over all saidrandomly selected orientations; and J) Iterating steps D) to I) for atleast N iterations or until M independent calculations of the averagedcross sectional area agree within a predetermined range R for Xiterations wherein at least steps D) to I) are preformed with ansufficiently programed computer.
 4. The system according to claim 3wherein the method correlates the differences in the molecularstructures with differences in the activity of drugs.
 5. The systemaccording to claim 4 wherein said drugs are organometallic based drugs.6. The system according to claim 5 wherein said organometallic baseddrugs are anti-cancer drugs.
 7. The system according to claim 5 whereinthe organometallic based drugs are isomeric Ru-based.
 8. The systemaccording to claim 3 wherein the ion mobility cell generates atravelling wave and the IM-MS technique includes travelling wave(T-wave) mobility separation.
 9. A system for determiningcharacteristics of predetermined molecules, the system comprising: anion mobility cell; a mass spectrometer; and a processor programmed orconfigured to determine experimentally, values of a range of molecularstructures and compare the values of the range with those derived by amethod of estimating a cross-sectional area of a molecule of interest soas to correlate differences in the molecular structures with differencesin selected predetermined activity of those molecules.